Question

A particular isotope has a​ half-life of 55 days. If you start with 1 kilogram of this​ isotope, how much will remain after 120 ​days? after 240 ​days? ​(Round to three decimal places as​ needed.)

Answer 1

Given the half-life, you have enough information to find the decay factor $k$ that satisfies

$\dfrac12=e^{55k}\implies k=-\dfrac{\ln2}{55}\approx-0.013$

Starting with 1 kg of the isotope, after 120 days you would be left with

$y=e^{120k}=\dfrac1{2^{24/11}}\approx0.220\text{ kg}$

After 240 days, you would have

$y=e^{240k}=\dfrac1{2^{48/11}}\approx0.049\text{ kg}$